Ditching-rotary tiller was widely used in tillage and ditching furrow during rapeseed sowing. As its ditching furrow system (consist of four identical ditching plows) would bear great drag resistance from the soil during operation, the ditching plow was optimized based on differential geometry analysis and EDEM simulation. Resistance-velocity simulation indicated the plow with parabolic type guide curve had better reduce-drag characteristics. Differential geometry analysis indicated decay rate of E and growth rate of G could represent the variable regularity of drag resistance with the increase of velocity. The L value could represent the magnitude of drag resistance. The smaller L value, decay rate of E and growth rate of G, the better drag-reduce characteristics. Quadratic rotation orthogonal combination design shown the optimal structural parameter values were: Δθ=15°, θmin=45°, h=250mm, l=100mm. The minimum average drag resistance was 230.1N. The differential geometry analysis of optimal ditching plow shown |dE/dκ| and |dG/dκ| could obtain minimum value, indicating growth rate of drag resistance for optimal plow was the lowest within the experimental level. Field experiment indicated the operation effect of optimized ditching furrow system could met the requirements of rapeseed sowing. The research provided in-depth theoretical guidance for Drag-reduce design of plow.

This study presents a novel approach for quantifying the dynamics of monthly hydraulic geometry relationships in the Jingjiang reach of the Yangtze River by integrating leaf area index (LAI) data as an indicator of riparian vegetation. A comprehensive system of ordinary differential equations (ODEs) couples traditional power-law hydraulic geometry equations with LAI, capturing the influence of erosion control on channel morphology. The periodic delayed response theory and automatic differentiation techniques are employed to enhance the modeling framework's capabilities. Calibration and verification demonstrate the models' effectiveness in capturing overall trends in discharge, width, and depth dynamics, outperforming traditional constant-parameter approaches. However, model predictive abilities are limited under extreme climate conditions due to training on normal climate data. Key assumptions, including the periodic delayed response theory's neglect of peak discharges, simplified representation of artificial cut-offs, and reliance on remotely sensed data with limited local validation, introduce uncertainties. The proposed modeling framework shows potential for broader application to other river systems with appropriate adjustments. Future research could incorporate additional environmental factors, integrate models across scales, couple with advanced simulation techniques, and expand stability assessments beyond the riverbed index. By addressing related challenges, this integrated approach lays a foundation for enhancing understanding of river morphodynamics and channel stability.

Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser algebraic topology is fixed. Should the spacetime we reside in takes up one of the more exotic choices, and there is no obvious reason why it shouldn't, apparent pathologies would inevitably plague calculus-based physical theories assuming the standard vanilla structure, due to the non-existence of a diffeomorphism and the consequent lack of a suitable portal through which to transfer the complete information regarding the exotic physical dynamics into the vanilla theories. An obvious plausible consequence of this deficiency would be the uncertainty permeating our attempted description of the microscopic world. We tentatively argue here, that a re-inspection of the key ingredients of the phenomenological particle models, from the perspective of exotica, could possibly yield interesting insights. Our short and rudimentary discussion is qualitative and speculative, because the necessary mathematical tools have only just began to be developed.

The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with con-strains to get an analytically approximate solution for the ODE under consider-ation. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

The pollution caused by nitrogen dioxide is a major environmental problem in China. This study introduces a new type of atmospheric trace gas remote-sensing instrument, an airborne fiber imaging spectrometer. This spectrometer has a spectral range of 300–410 nm and works in push-broom mode with a 30° field of view on a flight path. Flight experiments were conducted on December 30, 2022 and January 5, 2023, covering heavily polluted areas of east of Beijing and Tangshan. This equipment obtained the density distribution of NO2 over the flight area. The results showed that pollution was mainly concentrated in the Caofeidian area and at the power station in the north, and the main source of pollution was anthropogenic. Satellite and airborne data near the pollution points were compared, and the two datasets showed a positive correlation with a correlation coefficient of 0.78 and 0.7, on the two days, respectively. This study demonstrates the capability of an airborne fiber imaging spectrometer for NO2 regional emission remote sensing and identifying the pollution points.

This research presents a solution to the problem of planning the optimum area for economic crops by developed mathematical models and developed an algorithm to solve the problem of planning the optimum area by considered economic value for the maximize profit of farmers. The data were collected from farmers in 8 provinces in the northeastern region of Thailand. The 3 economic crops studied were rice, cassava and sugarcane. The solving problem methods were 1) Created mathematical models and solved the problems with Lingo V.11. 2) Improved Differential Evolution algorithms (I-DE) to solve the problems, which had 3 local search methods included (Swap, Cyclic Move and K-variable moves). The results of this study showed that in the small and medium problems instances, Lingo V.11 and DE provided equal profit outcome but DE was faster but in the large size of test instances DE generated better solution than that of Lingo v.11 when Lingo simulation time is set to 250 hours and DE simulation time has set to maximum 21.82 minutes. 2) Comparing DE and I-DE , I-DE outperforms DE in finding the better solution for all size of test instances (small, medium and large).

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

In this paper, we employ fuzzy Sumudu transform for solving system of linear fuzzy differential equations with fuzzy constant coefficients. The system with fuzzy constant coefficients is interpreted under strongly generalized differentiability. For this purpose, new procedures for solving the system are proposed. A numerical example is carried out for solving system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.

We discuss a remote sensing system that is used to simultaneously detect range-resolved differential absorption LIDAR (light detection and ranging; DIAL) signals and integrated path DIAL signals (IP-DIAL) from aerosol targets for ranges up to 22 km. The DIAL/IP-DIAL frequency converter consists of an OPO pumped at 1064 nm to produce light at 1.6 μm and operates at 100 Hz pulse repetition frequency. The probe light is free space coupled to a movable platform that contains one transmitter and two receiver telescopes. Hybrid photon counting/current systems increase the dynamic range for detection by two orders of magnitude. Range resolved and column integrated dry-air CO2 and CH4 mixing ratios are obtained from line shape fits of CO2 and CH4 centered at 1602.2 nm and 1645.5 nm, respectively and measured at 10 different frequencies over ≈ 1.5 cm-1 bandwidth. The signal-to-noise ratios (SNR) of the IP-DIAL returns from cloud aerosols approach 1000:1 and the uncertainties in the mixing ratios weighted according to the integrated counts over the cloud segments range from 0.1 % to 1 %. The range averaged DIAL mixing ratios are in good agreement with the IP-DIAL mixing ratios at the 1 % to 2 % level for both CO2 and CH4. These results can serve as a validation method for future active and passive satellite observational systems.

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

The intricate relationship between genomic mutations and proteomic network topology represents a frontier in understanding cellular resilience and disease mechanisms. This study presents a novel approach to analyzing how proteomic topological structures evolve and potentially break down in response to accumulating genomic mutations, offering insights into the complex interplay between genetic alterations and protein interaction networks. We developed a computational model simulating a network of ten key proteins (A-J) over 20 discrete time points, each representing a state of increasing genomic mutation load. Our model incorporates dynamic protein interaction strengths that fluctuate in response to simulated genomic alterations and a topological representation of the protein network, allowing for visualization of structural changes. Not forgetting a quantitative measure of network integrity, correlating with the system's ability to maintain function under mutational stress. Our Key findings include: visualization of proteomic network evolution through a series of topological graphs, revealing how genomic mutations progressively alter protein interaction patterns and identification of a critical "breakage point" in the network topology, signifying a threshold where genomic mutations overwhelm the protein network's ability to maintain its functional structure. And also quantification of network properties, including interaction strengths and overall network density, demonstrating the non-linear relationship between genomic mutations and proteomic topological integrity.The observed breakage point may represent a critical threshold in disease progression, where the accumulation of genomic mutations leads to a collapse in the proteomic interaction network, potentially triggering pathological states. This methodology offers a new perspective on the genotype-phenotype relationship, viewing it through the lens of protein network topology. Our approach provides a framework for future studies to analyze how specific genomic mutations might impact proteomic structures, potentially leading to new insights in cancer research, neurodegenerative disorders, and other mutation-driven diseases. It also suggests that maintaining proteomic topological integrity could be a key factor in cellular resilience against genomic instability.

Calculus, as a starting point to everyone's study of mathematics, was developed along with classical mechanics. Though not rigorously formulated, the intuition for differential form and infinitesimal motion makes calculus not hard to understand. And hence it does not require great effort to grasp the principles of classical mechanics. However, the situation becomes quite different when it comes to the quantum world. Given a particle system, what of interest is always the physical quantity of this system, such as energy, position, momentum, entropy, etc. But it is no longer straightforward.

Molecular studies regarding regulatory elements such as small ncRNAs and their mechanisms are poorly understood in infectious diseases. Tuberculosis is one of the oldest infectious diseases of humanity, and it is still a challenge to prevent and treat it. The control of the infection as well as its diagnosis are still complex, and treatments used are linked to several side effects. This study aimed to investigate miRNA’s expression profile to identify possible biomarkers for tuberculosis. We applied NGS techniques to investigate miRNA’s global expression profile from blood samples of infected patients with tuberculosis, their respective healthy physicians, and external healthy individuals as controls. Samples from 22 individuals run through a differential expression, target genes, gene set enrichment, and miRNA-gene network analysis. We observed 153 altered miRNAs, among which, only three DEmiRNAs (hsa-let-7g-5p, hsa-miR-486-3p and hsa-miR-4732-5p) were found between the investigated patients and their respective physicians. These DEmiRNAs are suggested to play an important role in granuloma regulation and their immune physiopathology. Our results propose that miRNAs may be involved in immune modulation, regulating the repertoire of genes expressed in the immune system’s cells. Our findings encourage the application of miRNAs as potential biomarkers for tuberculosis.

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

In this study, a design of Morlet wavelet neural networks (MWNNs) is presented to solve the prediction differential model (PDM) using the global approximation capability of genetic algorithm (GA) and local quick interior-point algorithm scheme (IPAS), i.e., MWNN-GAIPAS. The famous PDM is known as a variant of functional differential system that works as an opposite of the historical delay differential models. A fitness function is optimized using the mean square error by applying the GA-IPAS for solving the PDM. Three PDM examples have been presented numerically to check the authenticity of the MWNN-GAIPAS. For the perfection of the designed MWNN-GAIPAS, the comparability of the obtained results and exact results is performed. Moreover, the neuron analysis is performed by taking the 3, 10 and 20 number of neurons. The statistical observations have been performed to authenticate the reliability of the MWNN-GAIPAS for solving the PDM.

We propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.

Background/Objectives: The differential diagnosis of tuberculosis (TB) and lung cancer (LC) is often challenging due to similar clinicopathological presentations when bacterial shedding is negative, which can lead to delays in treatment. In this study, we tested the potential of plasma-circulating microRNAs (miRNAs) for the early and differential diagnosis of TB and LC. Methods: We conducted a two-phase study: profiling 188 miRNAs in pooled plasma samples and validating 14 selected miRNAs in individual plasma samples from 68 LC patients, 38 pulmonary TB patients, and 41 healthy controls. Results: Twelve miRNAs were significantly elevated in LC patients compared to controls and TB patients, while two miRNAs were significantly elevated in TB patients compared to controls. ROC analysis demonstrated that miR-130b-3p, miR-1-3p, miR-423-5p, and miR-200a-3p had good discriminatory ability to distinguish LC patients (including those with stage I tumours) from healthy individuals and miR-130b-3p, miR-423-5p, miR-15b-5p, and miR-18b-5p effectively distinguished LC patients (including those with stage I tumours) from TB patients. Additionally, miR-18b-5p showed good discriminatory ability between SCLC and NSCLC patients. Conclusions: Circulating miRNAs hold strong potential for the early detection of LC and for distinguishing LC from TB.

The Normalized Differential Spectral Attenuation (NDSA) technique was proposed years ago as an active method for measuring Integrated Water Vapor (IWV) along a Ku/K-band radio link immersed (totally or partially) in the troposphere. The approach is of the active kind, as it relies on the transmission of a couple of sinusoidal signals, whose power is measured at the receiver, thus providing the differential attenuation measurements from which IWV estimates can be in turn derived. In 2018, a prototype instrument providing such differential attenuation measurements was completed and set up for a first measurement campaign aimed at demonstrating the NDSA method. By the end of June 2022, the instrument was profoundly modified and upgraded so that a second measurement campaign could be carried out from August 1 to November 30, 2022. The transmitter was placed on the top of Monte Gomito (44.1277°lat, 10.6434°lon, 1892 m a.s.l.) and the receiver on the roof of the Department of Information Engineering of the University of Florence (43.7985°lat, 11.2528°lon, 50 m a.s.l.). The resulting radio link length was 61.15 km. Four ground weather stations of the regional weather service were selected among those available. In this paper, we describe the upgraded instrument and present the outcomes of the new measurement campaign, whose purpose was mainly to compare the IWV estimates provided by the instrument with the ground sensors measurements of air temperature, air humidity, barometric pressure, and rainfall.

Long non-coding RNAs (lncRNAs) are involved in numerous biological processes and serve crucial regulatory functions in both animals and plants. Nevertheless, there is limited understanding of lncRNAs and their patterns of expression and roles in sharks. In the current study, we systematically identified and characterized lncRNAs in the blue shark Prionace glauca from four tissues (liver, spleen, muscle, and kidney) using high-throughput sequencing and bioinformatics tools. A total of 21,932 high confidence lncRNAs were identified with 8,984 and 3,067 stably and tissue-specific expressed lncRNAs, respectively. In addition, a total of 45,007 differentially expressed (DE) lncRNAs were obtained among tissues, with kidney versus muscle having the largest numbers across tissues. DE lncRNAs trans target protein-coding genes were predicted, and functional gene ontology enrichment of these genes showed GO terms such as muscle system processes, cellular/metabolic processes, and stress and immune responses, all of which correspond with the specific biological functions of each tissue analyzed. These results advance our knowledge of lncRNAs in sharks and present novel data on tissue-specific lncRNAs, providing key information to support future functional shark investigations.

Neural Fractional Differential Equations (Neural FDE) represent a neural network architecture specifically designed to fit the solution of a fractional differential equation to given data. This architecture combines an analytical component, represented by a fractional derivative, with a neural network component, forming an initial value problem. During the learning process, both the order of the derivative and the parameters of the neural network must be optimised. In this work, we investigate the non-uniqueness of the optimal order of the derivative and its interaction with the neural network component. Based on our findings, we perform a numerical analysis to examine how different initialisations and values of the order of the derivative (in the optimisation process) impact its final optimal value. Results show that the neural network on the right-hand side of the Neural FDE struggles to adjust its parameters to fit the FDE to the data dynamics for any given order of the fractional derivative. Consequently, Neural FDEs do not require a unique α value, instead, they can use a wide range of α values to fit data. This flexibility is beneficial when fitting to given data is required, and the underlying physics is not known.

Antiangiogenic therapy (AAT) is an indirect oncological modality which is aimed at disruption of cancer cells nutrient supply. Invasive tumors have been shown to possess inherent resistant to this treatment, while compactly growing benign tumors react to it by shrinkage. It is generally accepted that AAT by itself is not curative. This study presents a mathematical model of non-invasive tumor growth with physiologically justified account of alteration of microvasculature and biomechanical aspects during tumor growth and AAT. In untreated setting the model reproduces tumor growth with saturation, where the maximum tumor volume depends on the level of angiogenesis. The outcomes of simulations of AAT depend on the tumor size at the moment of treatment initiation. If it is close to the stable size of avascular tumor grown in absence of angiogenesis, then the tumor is rapidly stabilized by AAT. Treatment of large tumors is accompanied by displacement of normal tissue due to the tumor shrinkage. During it, microvasculature undergoes distortion which degree depends on the displacement distance. As it affects tumor nutrient supply, the stable size of a tumor that undergoes AAT negatively correlates with its size at the beginning of treatment. For sufficiently large initial tumors, the long-term survival of tumor cells is compromised by competition with normal cells for severely limited inflow of nutrients, which makes AAT effectively curative.

In this work, the analytical treatment of Fourth order pd equations has been discussed with the variational iteration algorithm with an auxiliary parameter. The technique has the capability of reducing the size of computational work and easily overcomes the difficulty of the perturbation method or Adomian polynomials. Comparison with the classic variational iteration algorithm- is carried out, showing that the modification is more efficient and reliable.

Background: By using outcome prediction scores, it is possible to distinguish between good and poor performers with cochlear implants (CI) after CI implantation. The reasons for poor performance, despite good basic conditions, can be manifold. On the one hand, the postoperative fitting may be inadequate; on the other, neurophysiological disease processes may impair speech understanding with a CI. These disease processes are not yet fully understood. In acoustics, it is known that the auditory brainstem responses (ABR) and their latencies and amplitudes allow differential diagnosis based on reference values for normal-hearing individuals. The aim of this study was to provide reference values for electrically evoked brainstem responses (EABRs) in terms of rate-dependent latencies and amplitudes. Methods: 20 experienced adult CI recipients with a predicted and measured good postoperative word recognition score were recruited from the clinic’s patient pool. In the same stimulation mode and intensity we measured latencies and interpeak-latencies of EABRs and electrically evoked compound action potentials (ECAPs). With a defined supra-threshold stimulation intensity above the individual ECAP threshold, we applied stimulation at several rates between 11 and 91 stimuli per second. Results: We found rate dependences for EABR latency t3 and t5 in the order of 0.19 ms and 0.37 ms respectively, while ECAP was not affected by rate. Correspondingly, the interpeak intervalls’ rate dependences for t5-t1, t5-t3 and t3-t1 were of the order of 0.37 ms, 0.18 ms and 0.19 ms. Comparing the EABR amplitudes between the stimulation rates 11/s and 81/s, we found that at 81/s the amplitudes were significantly reduced down: to 73% for A3 and 81% for A5. These rate dependences of latency and amplitude in EABR have characteristics comparable to those of acoustic ABR. Conclusions: These data may serve to provide reference values for EABR and ECAP latencies, interpeak intervals and amplitudes with respect to stimulation rate. Altered response patterns of ECAPs and EABRs to normalised stimulation modes could be used in the future to describe and classify neuropathological processes in a better-differentiated way.

The core reasoning task for datalog engines is materialization, the evaluation of a datalog program over a database alongside its phys- ical incorporation into the database itself. The de-facto method of computing it, is through the recursive application of inference rules. Due to it being a costly operation, it is a must for datalog engines to provide incremental materialization, that is, to adjust the computation to new data, instead of restarting from scratch. One of the major caveats, is that deleting data is notoriously more involved than adding, since one has to take into account all possible data that has been entailed from what is being deleted. Differential Dataflow is a computational model that provides efficient incremen- tal maintenance, notoriously with equal performance between ad- ditions and deletions, and work distribution, of iterative dataflows. In this paper we investigate the performance of materialization with three reference datalog implementations, out of which one is built on top of a lightweight relational engine, and the two others are differential-dataflow and non-differential versions of the same rewrite algorithm, with the same optimizations.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

This study aims to implement a SSDBI (single-stage differential boost inverter, SSDBI) applying in a single-stage BESS (battery energy storage system, BESS) topology, which can supply power from lower voltage battery module to AC load. Compared with the common two-stage topology, which has a two-stage converter and higher voltage battery module array, the single-stage topology can reduce the number of cells and components, and improve the power density. In addition, a modified SPWM control was proposed to reduce the control complexity of the SSDBI while improving the THD of the inverter. The modified SPWM control can reduce the duty ratio of the SSDBI and the stress on the components to improve the AC voltage output waveform and reduce the THD value about 2.654%.

Image segmentation and classification still represent an active area of research since no universal solution can be identified. Established segmentation algorithms like thresholding are problem specific, treat well the easy cases and mostly relied on single parameter i.e intensity. Machine learning approaches offer alternatives where predefined features are combined into different classifiers. On the other hand, the outcome of machine learning is only as good as the underlying feature space. Differential geometry can substantially improve the outcome of machine learning since it can enrich the underlying feature space with new geometrical objects, called invariants. In this way, the geometrical features form a high-dimensional feature space for each pixel, where original objects can be resolved. Alternatives based on the geometry of the image scale-invariant interest points have been exploited successfully in the field of computer vision. Here, we integrate geometrical feature extraction based on signal processing, machine learning, and input relying on domain knowledge. The approach is exemplified on the ISBI 2012 image segmentation challenge data set. As a second application, we demonstrate powerful image classification functionality based on the same principles, which was applied to the HeLa and HEp-2 data sets. Obtained results demonstrate that feature space enrichment properly balanced with feature selection functionality can achieve performance comparable to deep learning approaches.

Background: Traditional omic analysis relies on p-value and fold change as selection criteria. There is an ongoing debate on their effectiveness in delivering systemic and robust interpretation, due to their dependence on assumptions of conformity with various parametric distributions.Here, we propose a threshold-free selection method based on robust, non-parametric statistics, ensuring independence from the statistical distribution properties and broad applicability. Such methods could adapt to different initial data distributions, contrary to statistical techniques based on fixed thresholds. Methods: Our work extends the Rank Products methodology with a neutral selection method of high information-extraction capacity. We introduce the calculation of the RP distribution’s entropy to isolate the features of interest by their contribution to the distribution’s information content. The aim is a methodology performing threshold-free identification of the differentially expressed features, which are highly informative about the phenomenon under scrutiny. Conclusions: Applying the proposed method on microarray (transcriptomic and DNA methylation) and RNAseq count data of varying sizes and noise presence, we observe robust convergence for the different parameterisations to stable cutoff points. Functional analysis through BioInfoMiner and EnrichR was used to evaluate the information potency of the resulting feature lists. Overall, the derived functional terms provide a systemic description highly compatible with the results of traditional statistical hypothesis testing techniques. The methodology behaves consistently across different data types. The feature lists are compact and information-rich, indicating phenotypic aspects specific to the tissue and biological phenomenon i nvestigated. Selection by information content measures efficiently addresses problems, emerging from arbitrary thresholding, thus facilitating the full automation of the analysis.

An easier method for the calibration of differential drive robots is presented. Most of the calibration is done on-board and it is not necessary to expend too much time taking note of the robot's position. The calibration method does not need a big free space to perform the tests. The bigger space is just in a straight line, which is easy to find. Results with the proposed method are compared with those from UMB as a reference, and they show very little deviation while the proposed calibration is much simpler.

In this paper, we investigate some kind of Dynkin game under $g$-expectation induced by backward stochastic differential equation (shortly for BSDE). We define the lower and upper value functions $\underline{V}_t=ess\sup\limits_{\tau\in{\mathcal{T}_t}} ess\inf\limits_{\sigma\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$ and $\overline{V}_t=ess\inf\limits_{\sigma\in{\mathcal{T}_t}}ess\sup\limits_{\tau\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$, respectively. Under some regular assumptions, a pair of saddle point is obtained and the value function of Dynkin game $V(t)=\underline{V}_t=\overline{V}_t$ follows. Furthermore, the constrained case of Dynkin game is also considered.

The (numerical) solution of Ordinary Differential Equations (ODEs) problems is of paramount relevance, ODEs system being an ubiquitous mathematical formulation of many physical phenomena (such as those involved in fluid dynamics, chemistry, biology, evolutionary-anthropology, ...): almost every dynamici phenomenon can be modeled by means of an ODEs system. The present paper is the first manifesto of FOODIE, a library aimed to numerically solve ODEs problems by means of a clear, concise and efficient abstract interface. FOODIE, meaning Fortran Object oriented Ordinary Differential Equations integration library, has manifolds aims: to provide a set to built-in numerical schemes that are accurate, robust, validated and efficient and to allow easy application of these schemes to (almost) all ODEs problems by means of an effective Abstract Calculus Pattern. The key idea is to allow the same solver-implementation to be applied to all ODEs problems thus avoiding the re-implementation of the ODEs solver for each different ODEs problem: code re-usability is consequently maximized, FOODIE being a general robust framework. Besides, the same framework also allows rapid development of new ODEs solvers due to the high abstraction level of the library itself. The present paper is the first announcement of FOODIE project: the current implementation is extensively discussed and its capabilities are proved by means of tests and examples.

Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on $SE(2)$. Here we extend these approaches to 3D using Fourier transform on the Lie group $SE(3)$ of rigid body motions. More precisely, we define the homogeneous space of 3D positions and orientations $\mathbb{R}^{3}\rtimes S^{2}:=SE(3)/(\{\mathbf{0}\} \times SO(2))$ as the quotient in $SE(3)$. In our construction, two group elements are equivalent if they are equal up to a rotation around the reference axis. On this quotient we design a specific Fourier transform. We apply this Fourier transform to derive new exact solutions to Fokker-Planck PDEs of $\alpha$-stable Lévy processes on $\mathbb{R}^{3}\rtimes S^{2}$. This reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions. We compare the exact probability kernel for $\alpha = 1$ (the diffusion kernel) to the kernel for $\alpha=\frac12$ (the Poisson kernel). We set up SDEs for the Lévy processes on the quotient and derive corresponding Monte-Carlo methods. We verify that the exact probability kernels arise as the limit of the Monte-Carlo approximations.

The endeavor to decode the brain's intricate architecture and its multifaceted functions has propelled scientists into the domain of complex differential equations, aiming to construct a computational framework capable of representing its uncountable intricacies. This article delves into the sophisticated and daunting task of modeling the brain, a system of seemingly uncountable coupled differential equations, each symbolizing the vast array of interconnected neural pathways and processes. We discuss the current limitations of computational resources and the significant challenges faced in accurately capturing the non-linear, high-dimensional, and plastic nature of neural dynamics. Despite these challenges, we explore the progressive strides in computational neuroscience that lay the groundwork for partial models, offering insights into the brain's localized circuits and broader network interactions. These models serve as pivotal stepping stones towards a more comprehensive understanding, which is incrementally built upon by interdisciplinary approaches, leveraging advancements in neuroimaging, data analysis, and theoretical biology. Looking ahead, the article speculates on the potential paradigm shifts that could arise from breakthroughs in computational technology, such as quantum computing, that may one day enable the simulation of the brain in its entirety. The article ultimately paints a picture of cautious optimism, where each incremental discovery is a valuable piece of the grand puzzle, bringing us closer to the epochal goal of comprehensively modeling the human brain.

This experimental research presents an easier model for fitting experimental results that can be simulate the dynamical behaviour of a single degree freedom system, SDFS, subjected in a forced vibration in a shaking table. The fractional damping using a Kelvin-Voigt fractional derivative rheological model, KVFRdm, to represent a fractional oscillator and compare with the experimental model.

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

We present a differentially private extension of the block coordinate descent based on objective perturbation. The algorithm iteratively performs linear regression in a federated setting on vertically partitioned data. In addition to a privacy guarantee, the algorithm also offers a utility guarantee; a tolerance parameter indicates how much the differentially private regression may deviate from an analysis without differential privacy. The algorithm’s performance is compared with the standard block coordinate descent algorithm and the trade-off between utility and privacy is studied. The performance is studied using both artificial test data and the forest fires data set. We find that the algorithm is fast and able to generate practical predictions with single-digit privacy budgets, albeit with some accuracy loss.

Alfalfa, an important legume forage, is an ideal crop for sustainable agriculture and a potential bioenergy plant. Drought, one of the most common environmental stresses, substantially affects plants’ growth, development and productivity. MicroRNAs (miRNAs) are newly discovered gene expression regulators that have been linked to several plant stress responses. To elucidate the role of miRNAs in drought stress regulation of alfalfa, a high-throughput sequencing approach was used to analyze 12 small RNA libraries comprising of 4 samples, each with 3 biological replicates. We identified 348 known miRNAs, belonging to 80 miRNA families, from the 12 libraries and 281 novel miRNAs using Mireap software. 18 known miRNAs in roots and 12 known miRNAs in leaves were screened out as drought-responsive miRNAs. Except for miR319d and miR157a which were upregulated under drought stress, the expression pattern of drought-responsive miRNAs were different between roots and leaves in alfalfa. This is the first study discovering miR157a, miR1507, miR3512, miR3630, miR5213, miR5294, miR5368 and miR6173 are drought-responsive miRNAs. Target transcripts of drought-responsive miRNAs were computationally predicted. All 447 target genes for the known miRNAs were predicted using an online tool. This study provides a significant insight on understanding drought-responsive mechanisms of alfalfa.

A nonlinear singularly perturbed Cauchy problem with confluent fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time. A similar initial value problem with logarithmic reliance in time has been investigated by the author in a recent work, for which sets of holomorphic inner and outer solutions were built up and expressed as a Laplace transform with logarithmic kernel. Here, a family of holomorphic inner solutions are constructed by means of exponential transseries expansions containing infinitely many Laplace transforms with special kernel. Furthermore, asymptotic expansions of Gevrey type for these solutions relatively to the perturbation parameter are established.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

This study developed a three-dimensional kinematic and dynamic model of a center-driven linkage system (CDLS). Force analysis was conducted to determine the required driving torque to ensure that the input link of the CDLS rotates at a constant speed with a certain angular velocity, even in the presence of frictional resistance torque. The primary objective was to optimize the maximum angular acceleration of the output links to reduce wiper noise. This optimization can enhance the stability of the linkage system while maintaining its operational functionality. In the adopted methodology, the frames of the fixed links are assumed to remain unchanged, and the input link is considered to operate at a constant angular speed and have a constant length. To meet standard vehicle windshield wiper requirements, 10 constraints were imposed on the optimization problem, which was solved using the differential evolution method. The lengths of both output links were reduced by over 10% after optimization.

This paper presents an enhanced Fully Connected Neural Network (FCNN) framework that incorporates manifold learning and Renormalization Group (RG) methods. By integrating Christoffel symbols, the model adapts to the curvature and topology of the data manifold, improving learning from geometrically complex data. Additionally, RG methods enable effective multi-scale data processing. We demonstrate the enhanced model’s performance on synthetic and real-world datasets, showing improved accuracy compared to standard FCNNs, particularly in complex systems simulation.

In this work, we study the equation of the catenary curve in the context of the Caputo derivative. We solve this equation and compare the solution with real physical models. From the experiments, we find that the best approximation is achieved in the classical case. Therefore, introducing a fractional parameter arbitrarily can be detrimental. However, we observe that when adding a certain weight to the chain, fractional calculus produces better results than classical calculus for modeling the minimum height.

Flap surgery is a common method used to cover defects following tumor ablation, trauma, or infection. However, insufficient vascularity in the transferred flap can lead to flap necrosis and failure. Proper postoperative monitoring is essential to prevent these complications. Recently, research has explored the use of infrared thermal imaging in plastic surgery, leading to its clinical application. This study investigates the use of a forward-looking infrared (FLIR) camera to monitor blood flow in flaps. In the study, 28 rats underwent reverse McFarlane flap surgery, and their flaps were analyzed using a FLIR thermal imaging camera seven days post-surgery. Additionally, thermal images of flaps were taken on postoperative days 0, 1, 2, 3, and 7 in 22 patients. The study focused on temperature differences between normal skin and the perforator compared to the average flap temperature. Results showed that the temperature difference was higher in the necrosis group and increased over time in cases of total necrosis. A lower perforator temperature compared to the flap's average indicated vascular compromise, potentially leading to flap failure. The FLIR camera, being contact-free and convenient, shows promise for understanding and inferring the clinical progression of flaps in postoperative monitoring.

Hydrodynamic resistance is a critical parameter in microfluidics, affecting device functionality and performance. However, quantifying hydrodynamic resistance in microfluidics is a challenge due to many influencing factors and the difficulties associated with the precise measurements of low flow rates (< 10 L/min) and pressure drops (< 5 kPa). This article presents a simple experimental test method for assessing hydrodynamic resistance, correlating with theoretical and numerical calculations. The results demonstrate good agreement between benchtop and theoretical data, suggesting a potential standardized method for assessing hydrodynamic resistance in microfluidic devices.

The susceptible-infected-recovered-vaccinated-deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encompasses the SIR, SIRV, SIRD, and SI models as special cases, with individual time-dependent rates governing transitions between different fractions. We investigate a special class of exact solutions and accurate analytical approximations for the SIRVD and SIRD compartment models. While the SIRVD and SIRD equations pose complex integro-differential equations for the rate of new infections and the fractions as a function of time, a simpler approach considers determining equations for the sum of ratios for given variations. This approach enables us to derive fully exact analytical solutions for the SIRVD and SIRD models. For nonlinear models with a high-dimensional parameter space, such as the SIRVD and SIRD models, analytical solutions, exact or accurately approximative, are of high importance and interest: not only as suitable benchmarks for numerical codes, but especially as they allow us to understand the critical behavior of epidemic outbursts as well as the decisive role of certain parameters. In the second part of our study, we apply a recently developed analytical approximation for the SIR and SIRV models to the more general SIRVD model. This approximation offers accurate analytical expressions for epidemic quantities, such as the rate of new infections and the fraction of infected persons, particularly when the cumulative fraction of infections is small. The distinction between recovered and deceased individuals in the SIRVD model affects the calculation of the death rate, which is proportional to the infected fraction in the SIRVD/SIRD cases but often proportional to the rate of new infections in many SIR models using a posteriori approach. We demonstrate that the temporal dependence of the infected fraction and the rate of new infections differs when considering the effects of vaccinations and when the real-time dependence of fatality and recovery rates diverge. These differences are highlighted for stationary ratios and gradually decreasing fatality rates. \Revised{The case of stationary ratios allows one to construct a new powerful diagnostics method to extract analytically all SIRVD model parameters from measured COVID-19 data of a completed pandemic wave.

The paper focuses on the different dynamical systems for the prey-predator model for different cases which includes greater depth of the food chain and varying number of preys and predators. We simulate the different postulated models and provide a comparative study for the same.

The global prevalence of type 2 diabetes mellitus (T2DM) has surged in recent decades and the identification of differential glycemic responders can aid tailored treatment for prevention of pre-diabetes and T2DM. A mixed meal tolerance test (MMTT) based on regular foods offers potential to uncover differential responders in dynamical postprandial events. We aimed to fit a simple mathematical model on dynamic postprandial glucose data from repeated MMTTs among partic-ipants with elevated T2DM risk, to identify response clusters and investigate their association with T2DM risk factors and gut microbiota. Data were used from a 12-week multi-center dietary inter-vention trial involving high-risk T2DM adults, comparing high- versus low-glycemic index foods within a Mediterranean diet context (MEDGICarb). Model-based analysis of MMTTs from 155 participants (81 females, 74 males) revealed two distinct plasma glucose response clusters that were associated with baseline gut microbiota. Cluster A, inversely associated with HbA1c and waist circumference and directly with insulin sensitivity, exhibited a contrasting profile to cluster B. Findings imply that a standardized breakfast MMTT using regular foods could effectively distin-guish non-diabetic individuals at varying risk levels for T2DM using a simple mechanistic model.

A diagnosis of typical chronic lymphocytic leukemia (CLL) requires the presence of ≥5000 clonal B-lymphocytes/μL with the coexistence of CD19, CD20, CD5, and CD23 and the restriction of light chain immunoglobulin, and the lack of expression of antigens CD22 and CD79b. Atypical CLL (aCLL) can be distinguished from typical CLL morphologically and immunophenotypically. Atypical CLL cells are defined as prolymphocytes; morphologically, these present as deeply-clefted lymphocytes which are larger than those in typical CLL, with condensed chromatin and without prominent nucleoli. However, current aCLL diagnostics rely more on immunophenotypic characteristics rather than atypical morphology. Immunophenotypically, atypical CLL differs from classic CLL in the lack of expression of one or fewer surface antigens, most commonly CD5 and CD23, and the patient does not meet the criteria for a diagnosis of any other B-cell lymphoid malignancy. Morphologically atypical CLL has more aggressive clinical behavior and worse prognosis than classic CLL. Patients with aCLL are more likely to display markers associated with poor prognosis, including trisomy 12, unmutated IGVH, and CD38 expression compared with classic CLL. However, no standard or commonly-accepted criteria exist for differentiating aCLL from classic CLL and the clinical significance of aCLL is still under debate. This review summarizes the current state of knowledge on the morphological, immunophenotypic and genetic abnormalities of aCLL.

A wide variety of renal neoplasms can have cystic areas. It happens for different reasons: some tumors have an intrinsic cystic architecture, others have a pseudocystic degeneration of necrotic foci or they have cystically dilated renal tubules constrained by stromal neoplastic cells. Clear cell renal cell carcinoma (CCRCC), either solid or cystic, is the most frequent type of renal cancer. While pseudocysts are found in high-grade aggressive CCRCC, cystic growth is associated to low-grade indolent cases. The latter also form through a cyst-dependent molecular pathway and they are more frequent in patients suffering from VHL disease. The differential diagnosis with multilocular cystic renal neoplasm of low malignant potential and clear cell papillary renal cell tumor can be especially hard and it requires a focused macroscopical and microscopical pathological analysis. As every class of renal tumors include cystic forms, a knowledge of criteria for a differential diagnosis is mandatory.

Polynomial recurrence bounds for a class of stochastic differential equations with a gradient type drift and an additive Wiener process are studied without Lyapunov functions.

Hessenberg differential algebraic equations (Hessenberg-DAEs) with high index play a critical role in the modeling of mechanical systems and multibody dynamics. Motivated by the widely used Lie Group Differential Algebraic Equation (LGDAE) method which only handles index 2 systems, we propose a Modified Extended Lie Group Differential Algebraic Equation (MELGDAE) method for solving index 3 Hessenberg-DAEs, and provide theoretical analysis to deepen the foundation of the MELGDAE method.The performance of the MELGDAE method is compared with the standard methods RADAU and MEBDF on index 2 and 3 DAE systems, and it is demonstrated that the MELGDAE integrator exhibits competitive performance in terms of high accuracy and the preservation of algebraic constraints. In particular, all differential variables in index 3 Hessenberg DAEs achieve second-order convergence using the MELGDAE method, which suggests potential for extension to Hessenberg-DAEs with an index of 4 or higher.

The study is devoted to the issues of mathematical modeling and simulating the sport differential mechanism (DM) with controllable torque redistribution. The issue is caused by the elaboration of ADAS systems with the automated torque vectoring for transmissions of all-wheel-drive (AWD) vehicles and the inclusion of such devices in the combined autonomous vehicle trajectory control scheme. At the article's beginning, the use of devices for redistributing traction forces is reasoned by analyzing the curvilinear vehicle motion, where they could ensure the accuracy of vehicle steerability. The literature review highlights modern developments in the field of modeling and researching such DMs. Considering the vehicle turn with a minimum radius, the conditions corresponding to passing greater torque over the outrunning rear axle are determined. All the mechanism's components and loads acting between them are described in detail. To form an original method of mathematical description of the mechanism functioning, the system of differential equations, systems of kinematic and force connections are considered separately. The article details the mathematical approach to generalize the way for automating the equation compilation for rotational mechanical systems such as vehicle transmissions. In the simulation section, a Simulink model reflecting the functional components and calculation procedures is presented. A series of testing and simulations on the DM operation with forcible torque distribution is carried out. Modeling data are presented, and the analysis of simulation results is performed. In the completion, conclusions are made regarding the scope and use of this model and the prospects for further developing the method proposed to automate the formation of equation systems.

Studies on the prevalence of Autism Spectrum Disorders show a gender disproportion. In the last years, there has been an increasing interest in the search for an explanation. There are two main lines of research; the first one looks for sex-related biological reasons that justifies the low prevalence of ASD in women (some protective factor related to hormones or immune system among others), and the second line of studies is related to the possible biases introduced in the diagnostic tools or procedures. In this article, a review of the latter line of research is made. Theoretical analysis following two objectives: a) Analysis of possible biases in diagnostic tools and b) Other non-biological explanations for gender differences in the prevalence of ASD. The literature analyzed provides contradictory results although it evidences the possible bias both in the construction of the diagnostic tools and in the assessment and determination of their standards. It is necessary to develop specific or complementary tools and diagnostic procedures differentiated by gender in order to control for this bias.

The main bottleneck when performing computational fluid dynamics (CFD) simulations of combustion systems is the computation and integration of the highly non-linear and stiff chemical source terms. In recent times, machine learning has emerged as a promising tool to accelerate combustion chemistry, involving the use of regression models to predict the chemical source terms as functions of the thermochemical state of the system. However, combustion is a highly nonlinear phenomenon, and this often leads to divergence from the true solution when the neural network representation of chemical kinetics is integrated in time. This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation (ODE) solvers. In this work, a novel neural ODE approach to combustion modeling, ChemNODE, is developed to address this issue. The source terms predicted by the neural network are integrated during training, and by backpropagating errors through the ODE solver, the neural network weights are adjusted accordingly to minimize the difference between the predicted and actual ODE solutions. It is shown that even when the dimensionality of the thermochemical manifold is trimmed to remove redundant species, the proposed approach accurately captures the correct physical behavior and reproduces the results obtained using the full chemical kinetic mechanism.

Rubbish in a forest environment is a great threat to this ecosystem, but this threat may also apply to the lost benefits for visitors to the forest. Previous studies proved that forest areas have a positive effect on obtaining psychological relaxation in the people visiting them. However, it was not known whether this restorative experience could be disturbed in any way by the presence of an open dump in the forest. To check how the presence of a landfill affects the visitors, an experiment was planned in which the respondents observed a forest area with a landfill and a forest landscape without a landfill for 15 minutes (control). The respondents then assessed the landscape using the semantic differential method and the Perceived Restorativeness Scale (PRS). An analysis of these observations showed that the presence of a landfill in the forest significantly changed the appreciation of the landscape by the respondents, the values of positive experiences decreased, and the negative experiences increased. Restorativeness was also reduced. Based on the results, it can be concluded that the presence of garbage in the forest may interrupt the restorative experience of its visitors.

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications emerged and became widely accepted, which generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAEs systems with large dimension, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on its Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameter has been presented.It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples. And numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.

The overwhelming majority of bladder cancers are transitional cell carcinomas. Albeit mostly monotonous, carcinomas in the bladder may occasionally display a broad spectrum of histological features that should be recognized by pathologists because some of them represent a diagnostic problem and/or lead prognostic implications. Sometimes these features are focal in the context of conventional transitional cell carcinomas, but some others are generalized across the tumor making its recognition a challenge. For practical purposes, the review distributes the morphologic spectrum of changes in architectural and cytological. So, nested and large nested, micropapillary, myxoid stroma, small tubules and adenoma nephrogenic-like, microcystic, verrucous, and diffuse lymphoepithelioma-like, on one hand, and plasmacytoid, signet ring, basaloid-squamous, yolk-sac, trophoblastic, rhabdoid, lipid/lipoblastic, giant, clear, eosinophilic (oncocytoid), and sarcomatoid, on the other, are revisited. Key histological and immunohistochemical features useful in the differential diagnosis are mentioned. In selected cases, molecular data associated with the diagnosis, prognosis, and/or treatment are also included.

A mathematical model, composed of two non-linear differential equations that describe the population dynamics of CD4 T cells in the human immune system, as well as viral HIV particles, is proposed. The invariance region is determined, classical equilibria stability analysis is performed using the basic reproduction number, and numerical simulations are carried out, in order to illustrate stability results. Later, the model is modified with a delay term, which describes the time that cells require for immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations, via auxiliary variable use. For the new model, equilibrium points are determined, their local stability is examined, and results are studied by way of numerical simulation.

Type-2 fuzzy sets were introduced by L. Zadeh aiming at modelling some settings in which fuzzy sets (usually called type-1 fuzzy sets) are not sufficient to reflect certain uncertainty degrees - loosely speaking, they are fuzzy sets whose membership degrees are ordinary fuzzy sets. On the other hand, fiber bundles are topological entities of extreme importance in Mathematics itself and many other scientific areas, like Physics (General Relativity, Field Theory etc.), finance modelling, and statistical inference. The present work introduces a conceptual link between the two ideas and conjectures about the potential mutual benefits that can be obtained from this viewpoint.As an objective and usable product of the presented ideas, it is described a framework for defining type-2 fuzzy hedges, proper to operate on interval type-2 fuzzy sets.

Because only two variables are needed to characterize a simple thermodynamic system in equilibrium, any such system is constrained on a 2D manifold. Of particular interest are the exact 1-forms on the cotangent space of that manifold, since the integral of exact 1-forms is path-independent, a crucial property satisfied by state variables such as internal energy dE and entropy dS. Our prior work [1] shows that given an appropriate language of vector calculus, a machine can re-discover the Maxwell equations and the incompressible Navier-Stokes equations from data. In this paper, We enhance this language by including differential forms and show that machines can re-discover the equation for entropy dS given data. Since entropy appears in various fields of science in different guises, a potential extension of this work is to use the machinery developed in this paper to let machines discover the expressions for entropy from data in fields other than classical thermodynamics.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly's Criterion can be incorporated into standard portfolio optimization models. The model developed here combines risk and return into a single objective function by incorporating a risk parameter. This model is then solved for a portfolio of 10 stocks from a major stock exchange using a differential evolution algorithm. Monte Carlo calculations are used to verify the accuracy of the results obtained from differential evolution. The results show that evolutionary algorithms can be successfully applied to solve a portfolio optimization problem where returns are calculated by applying Kelly's Criterion to each of the assets in the portfolio.

A series of conditions can mimic musculoskeletal infections on imaging, complicating their diagnosis and affecting the treatment. Depending on the anatomical location, different conditions can manifest with clinical and imaging findings that mimic infections. Herein we present a wide spectrum of the musculoskeletal disorders of the axial skeleton, long bones, peripheral joints and soft-tissue which may manifest as an infectious process, besides focusing on the potential mimics of osteomyelitis, septic arthritis and infectious spondylodiscitis that are common in clinical practice. We present the typical imaging characteristics of each musculoskeletal infection, followed by mimicking conditions.

Data security and user privacy concerns are increasingly gaining attention. Federated learning models based on differential privacy offer a distributed machine learning framework that protects data privacy; however, the added noise can impact the model's utility, making performance evaluation crucial. To optimize the balance between privacy protection and model performance, we propose the Adaptive Weight-Based Differential Privacy Federated Learning (AWDP-FL) framework. This framework processes model parameters from the perspectives of neural network layers and model weights. Initially, each participant trains the model locally. During iterative training, the clipping threshold is determined by selecting an adaptive weight coefficient, followed by adaptive gradient clipping to control the gradient magnitude. Subsequently, adaptive gradient updates are applied to the model, and dynamic Gaussian noise is introduced when uploading the parameters to protect participant privacy. The server aggregates these noise-perturbed parameters to update the global model. This framework ensures strong privacy protection while maintaining model accuracy. Theoretical analysis and experimental results validate the effectiveness of this framework under stringent privacy constraints.

Within the phenomenology of particle physics, the theoretical model of 4-zero textures is validated using a chi-square criterion that compares experimental data with the computational results of the model. Traditionally, analytical methods that often imply simplifications, combined with computational analysis, have been used to validate texture models. In this paper, we propose a new meta-heuristic variant of the differential evolution algorithm that incorporates aspects of the particle swarm optimization algorithm called "HE-DEPSO" to obtain chi-squared values are less than a bound value, which exhaustive and traditional algorithms cannot obtain. The results show that the proposed algorithm can optimize the chi-square function according to the required criteria. We compare simulated data with experimental data in the allowed search region, thereby validating the 4-zero texture model.

This study presents two interconnected mathematical models: one describing the stability and bifurcation dynamics of ecological biomes, and another simulating the progressive deformation and structural failure of a toroidal object. Both models explore topological changes in complex systems, bridging concepts from ecology, materials science, and mathematical physics. The first part introduces a dynamic model of ecological biomes, incorporating seasonal oscillations and external pressures. We define equations for topology updates, seasonal effects, and pressure impacts, culminating in a bifurcation condition that represents a critical shift in the biome's equilibrium state. This model provides insights into the resilience and tipping points of ecological systems under varying environmental stresses.The second part extends these concepts to a three-dimensional toroidal structure. We present parametric equations describing the torus geometry and develop a time-dependent deformation model that includes both stochastic and deterministic elements. A novel twisting deformation component enhances the realism of the structural changes. We define a critical threshold for maximum displacement, beyond which the torus undergoes structural failure, analogous to the bifurcation point in the biome model. Both models are implemented computationally, providing visual representations of the systems' evolution over time. The biome model illustrates the path to and consequences of bifurcation, while the torus simulation depicts the stages of deformation leading to structural break. This work contributes to the understanding of topological changes and critical transitions in both ecological and physical systems. By presenting these models in parallel, we highlight the universal nature of stability, bifurcation, and failure across different domains. The methodologies presented here have potential applications in ecology, materials science, structural engineering, and theoretical physics, offering a framework for studying the limits of system integrity under stress.

Novel freeform optical design methods can be classified in two categories, relevant to the generation of a starting point or to the development of new optimization tools. In this paper, we design a freeform TMA optimized with different surface representations using either a differential ray-tracer as a new optimization tool, or commercial ray tracer (ANSYS-ZEMAX OpticStudio) for comparison. For differential ray tracing, we use FORMIDABLE (Freeform Optics Raytracer with Manufacturable Imaging Design cApaBiLitiEs): an optical design library with differential ray tracing and NURBS optimization capabilities under European Software Community License (ESCL). NURBS allow to represent a freeform surface without needing any prior knowledge on the surface, such as the polynomial degree in polynomial descriptions. However, commercial optical design software are designed to optimize polynomial surfaces, but are not well-suited to optimize NURBS surfaces. This requires to use a custom optical design library. To demonstrate the interest of using NURBS representation, freeform telescopes are independently optimized with NURBS using FORMIDABLE, or XY polynomials with OpticStudio over different iteration cycles. We then compare the resulting systems using their RMS Field Maps to assess the optimization quality of each surface representation. We also provide a full-system comparison, including mirror freeform departures. This study shows that NURBS can be a relevant alternative to XY polynomials for freeform optimization of reflective 3-mirror telescopes.

Viral contamination in the aquaculture industry is a significant challenge that requires further research. Emerging evidence suggests that long noncoding RNAs (lncRNAs) play a role in regulating various biological processes, including immunity. However, most studies have focused on model organisms, and little is known about non-coding RNAs in the immune response to viral hemorrhagic septicemia (VHS) in rainbow trout. In this study, we investigated the listing of non-coding RNAs (ncRNAs) in rainbow trout challenged with VHS virus. We explored their potential role in defense-like responses based on transcriptomic analysis of the virus-treated and control groups. As a result of this research, 4207 lncRNAs were identified, of which 182 lncRNAs were differentially expressed between treated and untreated samples. Among 7753 lncRNA transcripts, 1920 were novel intergenic (class code “u”), and 3748 transcripts were potentially novel isoform of lncRNAs. Gene ontology analysis revealed biological pathways associated with the stress response and immune signaling. Pairs of genes such as TP63-MSTRG.62, IL10-MSTRG.9783, IL10-MSTRG.9784, TK1-MSTRG.22826, and MSTRG.17881-GLI1 showed cis interactions, while DOCK10-MSTRG.30015, MSTRG.36357-LOC101268921, and MSTRG.34190-ENPP2 showed trans interactions. In this study, the role of lncRNAs in regulating the expression of the target genes was clearly identified. This finding is consistent with the regulatory processes of immune system responses mediated by cytokines, as well as the regulation of oxygen levels in response to viral infection. The information presented here highlights the various regulatory mechanisms of lncRNAs in the expression of immune system genes in fish treated with VHS virus.

A one-dimensional model for fluid and solute transport in poroelastic materials (PEM) is studied. Although the model was recently derived and some exact solutions, in particular steady-state solutions and their applications, were studied, special cases occurring when some parameters vanish were not analysed earlier. Since the governing equations are nonintegrable in nonstationary case, the Lie symmetry method and modern tools for solving ODE systems are applied in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with new Lie symmetries are identified. Some of them have a highly nontrivial structure that cannot be predicted from a physical point of view or using Lie symmetries of other real-world models. Applying the symmetries obtained, multiparameter families of exact solutions are constructed, including those in terms of elementary and special functions (hypergeometric, Whittaker, Bessel and modified Bessel functions). A possible application of the solutions obtained is demonstrated and it is shown that some exact solutions can describe (at least qualitatively) the solute transport in PEM. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems.

Uncertain fractional differential equation (UFDE) is an excellent tool for describing complicated dynamic systems. This paper analyzes the valuation problems of currency option based on UFDE under optimistic value criterion. Firstly, an uncertain fractional currency model is formulated to describe the dynamics of foreign exchange rate. Then, the pricing formulae of European, American and Asian currency option are obtained under optimistic value criterion, respectively. Finally, numerical simulations are provided to illustrate the validity of our theoretical results.

Use of MS Excel as a platform for teaching simple iterative solution of partial differential equations runs into issues of reliability of the computation because of the large number of calculations required. This article documents the problem and an empirical solution. The cause of this unreliability was found by detailed examination of the numerical results from three simultaneous iterations. Computers of several types from different manufacturers were found to fail occasionally in updating variables in the numerical iteration. A simple work-around is suggested and was tested on several platforms.

Evolutionary algorithms find applicability in reinforcement learning of neural networks due to their independence from gradient-based methods. To achieve successful training of neural networks using evolutionary algorithms, careful considerations must be made to select appropriate algorithms due to the availability of various algorithmic variations. In Part1 and Part2, the author previously reported experimental evaluations on Genetic Algorithm and Evolution Strategy for reinforcement learning of neural networks, utilizing the Acrobot control task. This article constitutes Part3 of the series of comparative research. In this study, Differential Evolution is adopted as the third instance of major evolutionary algorithms. The experimental results show a statistically significant superiority of DE over both GA and ES (p < .01). In addition, DE exhibits its robustness to variations in hyperparameter configurations (the number of offsprings and generations). In the previous experiments, both ES and GA showed significant performance differences depending on the configurations, whereas in the experiment reported in this article, such differences are not detected for DE.

Tandemly organized rRNA genes are the typical example of a multigene family, where individual members evolve coordinately within but independently between species due to gene conversion and unequal crossing over. More frequently, in eukaryotic species with an inter-species hybrid origin, expression of unhomogenized rRNA genes from one progenitor is epigenetically silenced because of nucleolus dominance, and distinct rRNA genes may lose functionality and evolve faster. Interestingly, we obtained unusual ribosomal gene sequences from Oryza species that showed great diversity and did not appear in the present rice genomic sequence. The diversity of rDNA sequences indicated that the homogenization in rice is incomplete and explains the introgression of distinct rRNA gene families into ancestral rice genome before speciation and continent separation. The divergent large subunit (LSU) ribosomal genes are expressed, some of them differentially, depending on the N-fertilization of plants. Detection of differential transcripts of the rRNA genes suggested that rRNA gene families are not functionally equivalent. Phylogenetic analysis assigned Oryza species branching order to monocots, and monocot lineages probably have the same ecological origin by molecular clock calculation. Therefore, our results suggested that the geographical distances of continents separation cause barriers to the gene flow and homogenization among Oryza species which requires further explanation,

Alzheimer’s disease (AD) is the leading cause of dementia, characterised by beta-amyloid plaques, neurofibrillary tangles, and oxidative stress. Iron is suspected to enhance disease progression, and chelation may be a potential treatment. We propose that Aloysia citrodora Paláu (AC), a plant in the Verbenaceae family, can act as a moderate chelator of iron. It may reduce the effect of iron on beta-amyloid 1-42 (Aβ1-42) aggregation. Cyclic voltammetry (CV) and differential pulse voltammetry (DPV) were used to demonstrate that AC can interact with iron (II) and iron (III), the two most abundant forms of iron within the body. DPV was also used to characterise Aβ1-42 aggregation, and two main features were obtained. The first is the tyrosine peak (~0.6 V) decreased in magnitude over time, which is a sign of aggregation and folding. The other is a conglomerate of peaks at ~0 V, whose identity is unknown. Furthermore, iron (II) increased the rate of tyrosine peak depreciation, and the addition of AC negated this induced effect. This implied that iron (II) increases Aβ1-42 aggregation into higher order, and AC may be an effective countermeasure.

For a system that turns out to be inactive in time t, the past entropy is considered as an uncertainty measure for the past lifetime distribution. In this study, we consider a coherent system that includes n components and has the property that all the components of the system have failed at time t. To assess the predictability of the coherent system’s lifetime, we use the system’s signature to determine the Rényi entropy of its past lifetime. We study several analytical results, including expressions, bounds, and order properties for this measure.

We study the existence of positive solutions for a system of Hadamard fractional differential equations on an infinite interval with nonnegative nonlinearities, subject to coupled nonlocal boundary conditions which contain Hadamard fractional derivatives and Riemann-Stieltjes integrals. In the proof of the main results, we use the Guo-Krasnosel'skii fixed point theorem and the Leggett-Williams fixed point theorem.

Variable during practice is widely accepted to be advantageous for motor learning and therefor a valuable strategy to effectively reduce high-risk landing mechanics and prevent primary anterior cruciate ligament (ACL) injury. Few attempts have examined the specific effects of variable train-ing in athletes who have undergone ACL reconstruction. Thereby it is still unclear to what extent the variations in different sensor areas lead to different effects. Accordingly, we compared the effects of versatile movement variations (DL) with variations of movements with emphasis on disrupting visual information (VMT) in athletes who had undergone ACL reconstruction. For-ty-five interceptive sports athletes after ACL reconstruction were randomly allocated to a DL group (n= 15), VT group (n= 15) or control group (n= 15). The primary outcome was functional performance (Triple Hop Test). The secondary outcomes included dynamic balance (Star Excur-sion Balance Test (SEBT)), biomechanics during single-leg drop-landing task hip flexion (HF), knee flexion (KF), ankle dorsiflexion (AD), knee valgus (KV), and vertical ground reaction force (VGRF), and kinesiophobia (Tampa Scale of Kinesiophobia (TSK)) assessed before and after the 8-weeks of interventions. Data were analyzed be means of 3×2 repeated measures ANOVA fol-lowed by post hoc comparison (Bonferroni) at the significance level of p≤0.05. Significant group × time interaction effects, main effect of time and main effect of group were found for triple hop test, all eight directions of SEBT, HF, KF, AD, KV, VGRF and TSK. There was no significant main ef-fect of group in HF and triple hop test. Also, significant differences in triple hop test, seven direc-tions of SEBT, HF, KF, KV, VGRF and TSK were found between control group with the DL and VMT groups. Between group differences in AD and medial direction of SEBT were not signifi-cant. Also, there was no significant differences between VMT and control groups in triple hop test and HF variables. Both motor learning (DL and VMT) programs improved outcomes in patients after ACL reconstruction. Findings suggest that DL and VMT training programs lead to compa-rable improvements in rehabilitation.

Bismuth oxides are well-known electro-catalysts in fuel cells systems; they are usually used as anodic materials for the oxidation of low molecular weight alcohols. The utilization of BiO₂ and MnO₂ as catalysts in the pharmaceutical analysis is analytical method for the determination of heavy metal antibacterial agents in Pharmaceutical Dosage form is developed. The method is based on the voltammetric determination of heavy metal using Bidified platinum electrode by Bismuth oxide. The two components are oxidized at the Bidified electrode surface with the development of current that is linearly proportional to their concentrations in the range of 7.04*10^-7- 1*10^-3 M heavy metal. The oxidation reaction of the two components is pH-dependent, in which the buffer used is Britton-Robinson at pH = 7.00 where maximum peak current and maximum peak separation is obtained. The regression factors obtained from the calibration curves are 0.9812. The method of analysis was validated, where the limit of detection (LOD) and the limit of quantitation (LOQ) were calculated to be 1.44*10^-4 M, 4.36*10^-4 M and 1.27*10^-4 M, 3.84*10^-4 M respectively, the percentage recovery of both components was also calculated to 77 % for heavy metal.

Standard cell culture is routinely performed at supraphysiological oxygen concentrations (~18% O2). Conversely, oxygen levels in most tissues range from 1%–6% (physioxia). Such hyperoxic conditions can alter reactive oxygen species (ROS) production, energy metabolism, mitochondrial network dynamics, and response to drugs and hormones. The aim of this project was to investigate the transcriptional response to different oxygen levels and whether it is similar across cell lines, or cell-line specific. Using RNA-seq, we performed differential gene expression and functional enrichment analyses in four human cancer cell lines, LNCaP, Huh-7, PC-3, and SH-SY5Y cultured at either 5% or 18% oxygen for 14 days. We found that oxygen levels affected transcript abundance of hundreds of genes, with the affected genes having little overlap between cell lines. Functional enrichment analysis also revealed different processes and pathways being affected in each cell line. Interestingly, we found that the top differentially expressed genes are involved in cancer biology. Further, we observed several hypoxia-inducible factor (HIF) targets upregulated at 5% oxygen, suggesting a role of HIF at physiological oxygen conditions. Finally, oxygen strongly induced transcription of mitochondrial genes in most cell lines, in a cell-type specific manner too. We conclude that cellular response to oxygen is widely cell-type specific, emphasizing the importance of maintaining physioxia in cell culture.

Background: The reliability of a recent review of meningiomas in the archeologic record was difficult to assess, given the inverted sex ratio of the report and other contents apparently at variance with anatomical/medical findings in scientifically-identified cases. It therefore seemed appropriate to reexamine the nature of meningiomas and derive improve criteria for their recognition in the archeologic record and distinguish them from hemangiomas and bone marrow hyperplasia (recognized in the form of porotic hyperostosis). Methods: Medically-documented cases of meningiomas, hemangiomas and cranial bone marrow hyperplasia were examined to establish a macroscopic standard that distinguishing among them. Alleged cases in the archeologic record were examined for conformity with those criteria. Results: An en face pattern of uniform mesh with contained whorls appears pathognomonic for meningiomas. This contrasts with the non-uniform marrow expansion displacement of trabeculae in porotic hyperostosis and non-uniform vascular displacement of trabeculae in hemangiomas. Reassessment of past attributions revealed few cases of meningiomas that could be confidently diagnosed. Those identified has sex ratios parsimonious with medical literature reports. Conclusions: Criteria suggested for identifying meningiomas permits distinguishing from hemangiomas, bone marrow hyperplasia (porotic hyperostosis) and from the macroscopically-observable surface spicules characteristic of osteosarcomas. Examination for fulfillment of criteria for meningiomas and hemangiomas seems to provide a picture (including sex ratios) more parsimonious with the clinical literature, concluding that Cook and Danforth’s disparate ratios were related to less fastidious case selection. Additionally, confidence in recognizing porotic hyperostosis may be compromised because of apparent similar macroscopic alterations to those seen with hemangiomas.

Physicists have employed various approaches to solve the “paradox” and offered a consistent conclusion that the traveller twin is younger than the homebody twin. However, some authors attribute the cause of differential aging to acceleration, while others believe that acceleration should not be regarded as the source of differential aging, but frame switch is. So far there is no agreement on this issue. Actually, acceleration and frame switch should not be regarded as the source of differential aging. The author will introduce a thought experiment in which two very long spacecraft are moving in opposite directions at a speed close to the speed of light to discuss the real cause of differential aging. The author found that the real cause of differential aging in the twin “paradox” is because of the asymmetry of destination choice. People always choose their destinations in the universe rather than in spacecraft. The destinations are always stationary relative to the homebody twin and moving relative to the traveller twin. Once we choose a destination in a reference frame, the distance is the proper length in this reference frame, but the distance will contract in another moving reference frame, thus the recording time will be shorter.

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

Conventionally, partial differential equations (PDE) problems are solved numerically through discretization process by using finite difference approximations. The algebraic systems generated by this process are then finalized by using an iterative method. Recently, scientists invented a short cut approach, without discretization process, to solve the PDE problems, namely by using machine learning (ML). This is potential to make scientific machine learning as a new sub-field of research. Thus, given the interest in developing ML for solving PDEs, it makes an abundance of an easy-to-use methods that allows researchers to quickly set up and solve problems. In this review paper, we discussed at least three methods for solving high dimensional of PDEs, namely PyDEns, NeuroDiffEq, and Nangs, which are all based on artificial neural networks (ANNs). ANN is one of the methods under ML which proven to be a universal estimator function. Comparison of numerical results presented in solving the classical PDEs such as heat, wave, and Poisson equations, to look at the accuracy and efficiency of the methods. The results showed that the NeuroDiffEq and Nangs algorithms performed better to solve higher dimensional of PDEs than the PyDEns.

Molybdenum oxides is well-known electro-catalysts in fuel cells systems, they are usually used as anodic materials for the oxidation of low molecular weight alcohols. The utilization of Mo as catalysts in the pharmaceutical analysis is not common yet. In this study, bare glassy carbon electrodes were modified by the oxides by means of electrochemical deposition and the modified electrodes were used as catalysts for the electrochemical oxidation of hydrochlorothiazide (HCT). Well-resolved anodic peaks were reported for the analyzed pharmaceuticals when the Mo/GCE was utilized for the analysis of HCT. Analytical performance of the modified electrodes was evaluated based on the following statistical parameters; linearity ranges, correlation coefficients, limits of detection and quantitation, and recovery values. The prepared electrodes were used for the determination of the active ingredients in their pharmaceutical formulations and the reported activity was correlated to influence of the utilized pH on both structures of the used electrodes and the detected analytes.

A mathematical expression to describe cation absorption of root is expressed with simulation results. The root cells selectively emit H+ ions with active transport consuming ATPs to establish electrical gradient. The gradient promotes external positive ions to flow into the roots, while carries negatively charged particles with symport. In this paper, a mathematical model whose independent variables are the concentrations of external and internal cation is presented. This differential equation is induced from Ohm’s law. The equation has terms for plant physiology, ion’s physical and electrical properties, growth of plant, and interaction between the root and the surroundings. Simulation showed that the physiology-related coefficient has important role on nutrition absorption.

In the context of the French-German space lidar mission MERLIN dedicated to the determination of the atmospheric methane content, an end-to-end mission simulator is being developed. In order to check whether the instrument design meets the performance requirements, simulations have to count all the sources of noise on the measurements like the optical energy variability induced by speckle. Speckle is due to interference as the lidar beam are quasi monochromatic. Speckle contribution to the error budget has to be estimated but also simulated. In this paper, the speckle theory is revisited and applied to MERLIN double pulsed IPDA lidar and also to the DLR demonstrator CHARM-F. Results show: on the signal path, speckle noise depends mainly on the size of the illuminating area on ground; on the solar flux, speckle is fully negligible both because the pixel size and the optical filter spectral width; on energy monitoring path a decorrelation mechanism is needed to reduce speckle noise on averaged data. Speckle noises for MERLIN and CHARM-F can be simulated by Gaussian noises with only one random draw by shot separately for energy monitoring and signal paths.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

The present paper introduces a method of basis transformation of vector fields that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such as Hermite, Laguerre and Legendre polynomials. The method based on separated transformation of vector space basis by a set of operators that are equivalent to the formal basis transformation and connected to it by linear combination with projection operators. Applying the Forbenius covariants yields a general method that incorporates the Rodrigues formula as a special case in polynomial space. Using the Lie algebra modules, specifically , on polynomial space results in isomorphic algebras whose Cartan sub-algebras are Hermite, Laguerre and Legendre differential operators. Commutation relations of these algebras and Baker-Campbell-Hausdorff formula gives new formulas for special polynomials

We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter. We exhibit two distinguished finite sets of holomorphic solutions, so-called outer and inner solutions, by means of a Laplace transform with special kernel and Fourier integral. We analyze the asymptotic expansions of these solutions relatively to the perturbation parameter and show that they are (at most) of Gevrey order 1 for the first set of solutions and of some Gevrey order that hinges on the unfolding of the irregular singularity for the second.

A near-exact analytical solution of the statistical Susceptible-Infectious-Recovered (SIR) epidemics model for a constant ratio k0 of infection to recovery rates is derived. The derived solution is not of inverse form as the known solutions in the literature but expresses rather directly the three compartmental fractions S(τ ), I(τ ) and R(τ ) and thus the rate of new infections j(τ ) = S(τ )I(τ ) in terms of the single function U (τ ) and the reduced time τ (the time-integrated infection rate), involving the principal and non-principal branches of Lambert’s function. Exact analytical formulas for the peak time and the maximum fraction of I(τ ) are obtained proving that the rate of new infections peaks before the fraction of infected persons. Our analysis is not entirely analytically exact because the reduced time dependence of the function U (τ ) obeying a nonlinear integro-differential equation is only obtained approximately by expanding a double-exponential function to first-order at small reduced times, and employing an accurate simple approximation of the principal Lambert function at large times, respectively.

We deal with Ulam stability of second order periodic linear differential equations with periodic damping. Necessary and sufficient condition for the Ulam stability of second order periodic linear differential equations is obtained by giving an Ulam stability theorem and an Ulam instability theorem. These results extend the conclusions in relevant literature. In addition, for the situation of constant coefficients, the minimum Ulam constant is given.

Differential beamforming has attracted much research since it can utilize the array with small aperture size to form frequency-invariant beampatterns and achieve high directional gains. It has recently been applied to the linear loudspeaker array to produce a broadside frequency-invariant radiation pattern. However, designing steerable frequency-invariant beampatterns for the linear loudspeaker array has yet to be explored. This paper proposes a method to design the steerable differential beamformer with the linear loudspeaker array. We first determine the target differential beampatterns according to the desired direction, the main lobe width, and the beampattern order. Then, we transform the target beampattern into the modal domain for representation. The Jacobi-Anger expansion is subsequently used to design the beamformer so that the resulting beam pattern matches the target differential beam pattern. Furthermore, based on the criterion of minimizing the mean square error between the synthesized beam pattern and the ideal one, a multi-constraint optimization problem is formulated to calculate the optimal desired weighting vector. Simulations and experimental results show that the proposed method can achieve steerable frequency-invariant beamforming over 300 Hz – 4 kHz.

Identification the parameters of triple-diode electrical circuit structure of PV-module is a challenging issue and has been emphasized as an important research area. Accordingly, a hybrid evolutionary optimization algorithm is presented in this paper. Differential evolution algorithm (DEA) is hybridized with electromagnetism-like algorithm (EMA) in the mutation stage to enhance the reliability and efficiency of DEA. The presented algorithm is called differential evolution with integrated mutation per iteration (DEIMA). A new formula is presented to adapt the control parameters (mutation factor and crossover rate) of DEA and is based on a sigmoid function in terms of the current and previous fitness function values. Seven different experimental data sets are used to assess the performance of the proposed DEIMA. The results of the proposed PV modeling method are evaluated with other approaches in literature. According to different statistical criteria, DEIMA offered superiority in terms of root mean square error and main bias error by at least 5.4% and 10%, respectively, as compared to other methods. Furthermore, DEIMA needs 27.69 sec. as an average execution time less than other compared methods.

This paper introduces a novel decision-making approach grounded in insights into human visual perception of change. Modern technologies such as internet of things (IoT) provide us with large amounts of sensor data that need to be processed in real time and decisions made with a high degree of accuracy and reliability. Artificial intelligence (AI) methods are welcome in this context and need to be upgraded to meet actual challenges. While modern computing capabilities facilitate rapid data processing, the real-time demands of vast sensor data necessitate swift responses across the cyber chain, often leading to compromises in solution quality to circumvent combinatorial search complexities. Determining the adequacy of a solution entails varied approaches, often relying on heuristic methodologies. We illustrate our original approach with an example of a selected detail of a differential evolution algorithm, where we have to make a decision to adopt the best solution so far. We propose an approach inspired by human perceptual features that exploits the Weber-Fechner law to emulate human judgements, and offers a promising way to improve decision making in AI applications and real-time requirements fulfillment. Our proposed methodology demonstrates applicability across diverse AI scenarios involving numerical data, effectively mirroring human perception abilities.

This project aims to simulate and analyze population dynamics in evolutionary systems, using stochastic differential equations and probabilistic rules for crossbreeding and benefits. The study employs advanced computational techniques to model the evolution of populations over an extended period. Specifically, we explore a scenario with ten distinct groups, each starting with an equal population and evolving under defined genetic and cooperative behaviors. The simulation spans 1000 years, incorporating individual lifespans, stochastic updates, and probabilistic interactions. To ensure robustness and reliability, the study includes detailed statistical analysis, encompassing descriptive statistics, confidence intervals, and ANOVA tests. We further visualize the temporal behavior of populations and subpopulations, providing insights into the evolutionary dynamics and stability of the system. The results demonstrate the effectiveness of balanced cooperation and genetic diversity in maintaining stable population distributions. The project showcases the integration of mathematical modeling, statistical analysis, and computational simulations, contributing valuable insights into evolutionary biology and complex systems. It highlights the importance of interdisciplinary approaches in understanding and predicting population behaviors, with implications for both theoretical research and practical applications in fields such as ecology, genetics, probability and social sciences.

As screen sizes are becoming larger and larger, which are beyond human’s physical limitation for direct touching interaction, remote controls are inevitable. However, as techniques applied so far, inertial gyroscopes are susceptible to position inaccuracies, and gesture recognition is limited by cameras’ focus depth and viewing angle. Grating antenna light trapping technology will be an ideal candidate providing the ghost point problem for multipoint inputs can be solved. Therefore, we propose a differential amplitude modulation scheme for grating antenna based multi beam optical touch, which can recognize different incidence points. Where, the amplitude of the incident beams was coded with different pulse width at first. Then, after been trapped by the grating antenna and been transferred into currents by the lined detector arrays, the incident points of the individual beams were recognized and differentiated. The scheme was successfully verified on an 18-inch screen, where two-point optical touch with position accuracy error under 3mm and response time less than 7ms under modulation frequency of 10kHz on both incident beams are obtained. This work paves a practical way for remote multi-point touch, which can make digital mouse in consistent to the users pointing direction obeying natural three-point one ling aiming rule instantaneously.

Under suitable continuity and uniqueness conditions, solutions of an α order Caputo fractional boundary value problem are differentiated with respect to boundary values and boundary points. This extends well-known results for nth order boundary value problems. The approach used is a standard technique and makes heavy use of recent results for differentiation of solutions of Caputo fractional intial value problems with respect to initial conditions and continuous dependence for Caputo fractional boundary value problems.